GATE CSE 1995 | Question: 1.12

Question

What is the distance of the following code $000000$, $010101$, $000111$, $011001$, $111111$?

• A. $2$
• B. $3$
• C. $4$
• D. $1$

Answer 1

Distance (also called min-distance) of a block code is the minimum number of positions in which any two distinct codes differ. Here, min-distance occurs for the codes $2$ and $3$ and they differ only in $2$ positions. So, $d = 2$.

https://en.wikipedia.org/wiki/Block_code

Correct Answer: $A$

Comments

@ Arjun sir,

codes 2 & 4 also has distance 2. right?

 010101

    XOR

 011001

= 001100

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@Arjun Sir, do we need to check each codeword distance to every other codeword, or just go sequentially?

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every code with every other code.

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hamming distance table -

Answer 2

(A) Distance = minimum hamming distance = $2$.

$010101  ⊕  011001  =  001100$

Answer 3

Check the solution

Answer 4

Hamming distance = minimum distance between keywords.

Here minimum distance occur between 010101
and 011001

and Answer is 2